{"arxiv":1,"month":"06","year":"2025","file":[{"access_level":"open_access","file_name":"2025_PODC_ElHayek.pdf","file_id":"20115","relation":"main_file","date_updated":"2025-08-04T09:10:55Z","date_created":"2025-08-04T09:10:55Z","success":1,"file_size":2200347,"checksum":"52976d226f3f691aa519d71c1c718fa5","content_type":"application/pdf","creator":"dernst"}],"_id":"20051","acknowledgement":"This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (MoDynStruct, No. 101019564) and the Austrian Science Fund (FWF) grant DOI 10.55776/I5862,grant DOI 10.55776/I5982, and grant DOI 10.55776/P33775 with\r\nadditional funding from the netidee SCIENCE Stiftung, 2020–2024\r\nand the German Research Foundation (DFG), grant 470029389\r\n(FlexNets).","department":[{"_id":"MoHe"}],"tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"citation":{"ista":"El-Hayek A, Elsässer R, Schmid S. 2025. An almost tight lower bound for plurality consensus with undecided state dynamics in the population protocol model. Proceedings of the ACM Symposium on Principles of Distributed Computing. PODC: Symposium on Principles of Distributed Computing.","ieee":"A. El-Hayek, R. Elsässer, and S. Schmid, “An almost tight lower bound for plurality consensus with undecided state dynamics in the population protocol model,” in <i>Proceedings of the ACM Symposium on Principles of Distributed Computing</i>, Huatulco, Mexico, 2025.","mla":"El-Hayek, Antoine, et al. “An Almost Tight Lower Bound for Plurality Consensus with Undecided State Dynamics in the Population Protocol Model.” <i>Proceedings of the ACM Symposium on Principles of Distributed Computing</i>, Association for Computing Machinery, 2025, doi:<a href=\"https://doi.org/10.1145/3732772.3733505\">10.1145/3732772.3733505</a>.","chicago":"El-Hayek, Antoine, Robert Elsässer, and Stefan Schmid. “An Almost Tight Lower Bound for Plurality Consensus with Undecided State Dynamics in the Population Protocol Model.” In <i>Proceedings of the ACM Symposium on Principles of Distributed Computing</i>. Association for Computing Machinery, 2025. <a href=\"https://doi.org/10.1145/3732772.3733505\">https://doi.org/10.1145/3732772.3733505</a>.","apa":"El-Hayek, A., Elsässer, R., &#38; Schmid, S. (2025). An almost tight lower bound for plurality consensus with undecided state dynamics in the population protocol model. In <i>Proceedings of the ACM Symposium on Principles of Distributed Computing</i>. Huatulco, Mexico: Association for Computing Machinery. <a href=\"https://doi.org/10.1145/3732772.3733505\">https://doi.org/10.1145/3732772.3733505</a>","ama":"El-Hayek A, Elsässer R, Schmid S. An almost tight lower bound for plurality consensus with undecided state dynamics in the population protocol model. In: <i>Proceedings of the ACM Symposium on Principles of Distributed Computing</i>. Association for Computing Machinery; 2025. doi:<a href=\"https://doi.org/10.1145/3732772.3733505\">10.1145/3732772.3733505</a>","short":"A. El-Hayek, R. Elsässer, S. Schmid, in:, Proceedings of the ACM Symposium on Principles of Distributed Computing, Association for Computing Machinery, 2025."},"OA_type":"hybrid","external_id":{"arxiv":["2505.02765"]},"author":[{"last_name":"El-Hayek","orcid":"0000-0003-4268-7368","full_name":"El-Hayek, Antoine","first_name":"Antoine","id":"888a098e-fcac-11ee-aff7-d347be57b725"},{"full_name":"Elsässer, Robert","last_name":"Elsässer","first_name":"Robert"},{"last_name":"Schmid","full_name":"Schmid, Stefan","first_name":"Stefan"}],"article_processing_charge":"Yes (in subscription journal)","oa":1,"language":[{"iso":"eng"}],"OA_place":"publisher","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","project":[{"name":"The design and evaluation of modern fully dynamic data structures","call_identifier":"H2020","grant_number":"101019564","_id":"bd9ca328-d553-11ed-ba76-dc4f890cfe62"},{"name":"Static and Dynamic Hierarchical Graph Decompositions","_id":"bda196b2-d553-11ed-ba76-8e8ee6c21103","grant_number":"I05982"},{"name":"Fast Algorithms for a Reactive Network Layer","_id":"bd9e3a2e-d553-11ed-ba76-8aa684ce17fe","grant_number":"P33775"}],"abstract":[{"lang":"eng","text":"We revisit the majority problem in the population protocol communication model, as first studied by Angluin et al. (Distributed Computing 2008). We consider a more general version of this problem known as plurality consensus, which has already been studied intensively in the literature. In this problem, each node in a system of n nodes, has initially one of k different opinions, and they need to agree on the (relative) majority opinion. In particular, we consider the important and intensively studied model of Undecided State Dynamics.\r\nOur main contribution is an almost tight lower bound on the stabilization time: we prove that there exists an initial configuration, even with bias \\Delta = \\omega(\\sqrt{n\\log n}), where stabilization requires \\Omega(kn\\log \\frac {\\sqrt n} {k \\log n}) interactions, or equivalently, \\Omega(k\\log \\frac {\\sqrt n} {k \\log n}) parallel time for any k = o\\left(\\frac {\\sqrt n}{\\log n}\\right). This bound is tight for any k \\le n^{\\frac 1 2 - \\epsilon}, where \\epsilon >0 can be any small constant, as Amir et al.~(PODC'23) gave a O(k\\log n) parallel time upper bound for k = O\\left(\\frac {\\sqrt n} {\\log ^2 n}\\right)."}],"doi":"10.1145/3732772.3733505","publication_identifier":{"isbn":[" 9798400718854"]},"ddc":["000"],"date_published":"2025-06-13T00:00:00Z","type":"conference","publication":"Proceedings of the ACM Symposium on Principles of Distributed Computing","corr_author":"1","file_date_updated":"2025-08-04T09:10:55Z","date_created":"2025-07-21T08:16:15Z","date_updated":"2025-08-04T09:16:27Z","day":"13","publication_status":"published","oa_version":"Published Version","quality_controlled":"1","conference":{"location":"Huatulco, Mexico","end_date":"2025-06-20","start_date":"2025-06-16","name":"PODC: Symposium on Principles of Distributed Computing"},"ec_funded":1,"publisher":"Association for Computing Machinery","has_accepted_license":"1","title":"An almost tight lower bound for plurality consensus with undecided state dynamics in the population protocol model"}